%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO218+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 07:48:16 PM UTC 2025 % Result : Theorem 49.95s 50.16s % Output : Proof 50.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GEO218+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 11:32:08 EDT 2025 % 0.13/0.34 % CPUTime : % 49.95/50.16 SZS status Theorem for theBenchmark.p % 49.95/50.16 SZS output start Proof for theBenchmark.p % 49.95/50.16 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), Not (convergent_lines X X)) True % 49.95/50.16 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True % 49.95/50.16 Clause #14 (by assumption #[]): Eq (∀ (L M : Iota), Not (And (Not (convergent_lines L M)) (Not (unorthogonal_lines L M)))) True % 49.95/50.16 Clause #15 (by assumption #[]): Eq % 49.95/50.16 (∀ (L M N : Iota), % 49.95/50.16 And (Or (Not (convergent_lines L M)) (Not (unorthogonal_lines L M))) % 49.95/50.16 (Or (Not (convergent_lines L N)) (Not (unorthogonal_lines L N))) → % 49.95/50.16 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N))) % 49.95/50.16 True % 49.95/50.16 Clause #17 (by assumption #[]): Eq % 49.95/50.16 (Not % 49.95/50.16 (∀ (L M N : Iota), And (Not (convergent_lines L M)) (Not (unorthogonal_lines L N)) → Not (unorthogonal_lines M N))) % 49.95/50.16 True % 49.95/50.16 Clause #18 (by clausification #[2]): ∀ (a : Iota), Eq (Not (convergent_lines a a)) True % 49.95/50.16 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (convergent_lines a a) False % 49.95/50.16 Clause #32 (by clausification #[17]): Eq (∀ (L M N : Iota), And (Not (convergent_lines L M)) (Not (unorthogonal_lines L N)) → Not (unorthogonal_lines M N)) % 49.95/50.16 False % 49.95/50.16 Clause #33 (by clausification #[32]): ∀ (a : Iota), % 49.95/50.16 Eq % 49.95/50.16 (Not % 49.95/50.16 (∀ (M N : Iota), % 49.95/50.16 And (Not (convergent_lines (skS.0 0 a) M)) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 49.95/50.16 Not (unorthogonal_lines M N))) % 49.95/50.16 True % 49.95/50.16 Clause #34 (by clausification #[33]): ∀ (a : Iota), % 49.95/50.16 Eq % 49.95/50.16 (∀ (M N : Iota), % 49.95/50.16 And (Not (convergent_lines (skS.0 0 a) M)) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 49.95/50.16 Not (unorthogonal_lines M N)) % 49.95/50.16 False % 49.95/50.16 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 49.95/50.16 Eq % 49.95/50.16 (Not % 49.95/50.16 (∀ (N : Iota), % 49.95/50.16 And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 49.95/50.16 Not (unorthogonal_lines (skS.0 1 a a_1) N))) % 49.95/50.16 True % 49.95/50.16 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 49.95/50.16 Eq % 49.95/50.16 (∀ (N : Iota), % 49.95/50.16 And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 49.95/50.16 Not (unorthogonal_lines (skS.0 1 a a_1) N)) % 49.95/50.16 False % 49.95/50.16 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 49.95/50.16 Eq % 49.95/50.16 (Not % 49.95/50.16 (And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 49.95/50.16 (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 49.95/50.16 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 49.95/50.16 True % 49.95/50.16 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 49.95/50.16 Eq % 49.95/50.16 (And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 49.95/50.16 (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 49.95/50.16 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 49.95/50.16 False % 49.95/50.16 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 49.95/50.16 Eq % 49.95/50.16 (And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 49.95/50.16 (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 49.95/50.16 True % 49.95/50.16 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Eq (Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False % 49.95/50.16 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Eq (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) True % 49.95/50.16 Clause #42 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) True % 49.95/50.16 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) False % 49.95/50.16 Clause #80 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), convergent_lines a Y → Or (convergent_lines a Z) (convergent_lines Y Z)) True % 49.95/50.16 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), convergent_lines a a_1 → Or (convergent_lines a Z) (convergent_lines a_1 Z)) True % 49.95/50.16 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines a a_1 → Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True % 49.95/50.16 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), % 49.95/50.16 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True) % 50.02/50.18 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), % 50.02/50.18 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True)) % 50.02/50.18 Clause #90 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (M : Iota), Not (And (Not (convergent_lines a M)) (Not (unorthogonal_lines a M)))) True % 50.02/50.18 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota), Eq (Not (And (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1)))) True % 50.02/50.18 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), Eq (And (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False % 50.02/50.18 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), Or (Eq (Not (convergent_lines a a_1)) False) (Eq (Not (unorthogonal_lines a a_1)) False) % 50.02/50.18 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), Or (Eq (Not (unorthogonal_lines a a_1)) False) (Eq (convergent_lines a a_1) True) % 50.02/50.18 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) True) (Eq (unorthogonal_lines a a_1) True) % 50.02/50.18 Clause #96 (by superposition #[95, 43]): ∀ (a a_1 a_2 : Iota), Or (Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq True False) % 50.02/50.18 Clause #97 (by clausification #[15]): ∀ (a : Iota), % 50.02/50.18 Eq % 50.02/50.18 (∀ (M N : Iota), % 50.02/50.18 And (Or (Not (convergent_lines a M)) (Not (unorthogonal_lines a M))) % 50.02/50.18 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) → % 50.02/50.18 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N))) % 50.02/50.18 True % 50.02/50.18 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), % 50.02/50.18 Eq % 50.02/50.18 (∀ (N : Iota), % 50.02/50.18 And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) % 50.02/50.18 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) → % 50.02/50.18 Or (Not (convergent_lines a_1 N)) (Not (unorthogonal_lines a_1 N))) % 50.02/50.18 True % 50.02/50.18 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), % 50.02/50.18 Eq % 50.02/50.18 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) % 50.02/50.18 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) → % 50.02/50.18 Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2))) % 50.02/50.18 True % 50.02/50.18 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), % 50.02/50.18 Or % 50.02/50.18 (Eq % 50.02/50.18 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) % 50.02/50.18 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2)))) % 50.02/50.18 False) % 50.02/50.18 (Eq (Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2))) True) % 50.02/50.18 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), % 50.02/50.18 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) True) % 50.02/50.18 (Or (Eq (Or (Not (convergent_lines a_2 a)) (Not (unorthogonal_lines a_2 a))) False) % 50.02/50.18 (Eq (Or (Not (convergent_lines a_2 a_1)) (Not (unorthogonal_lines a_2 a_1))) False)) % 50.02/50.18 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), % 50.02/50.18 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False) % 50.02/50.18 (Or (Eq (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) False) % 50.02/50.18 (Or (Eq (Not (convergent_lines a_1 a_2)) True) (Eq (Not (unorthogonal_lines a_1 a_2)) True))) % 50.02/50.18 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), % 50.02/50.18 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False) % 50.02/50.18 (Or (Eq (Not (convergent_lines a_2 a_1)) True) % 50.02/50.18 (Or (Eq (Not (unorthogonal_lines a_2 a_1)) True) (Eq (Not (unorthogonal_lines a a_2)) False))) % 50.02/50.18 Clause #106 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 50.02/50.18 Or (Eq (Not (convergent_lines a a_1)) True) % 50.02/50.18 (Or (Eq (Not (unorthogonal_lines a a_1)) True) % 50.02/50.18 (Or (Eq (Not (unorthogonal_lines a_2 a)) False) (Eq (Not (convergent_lines a_2 a_1)) False))) % 50.02/50.18 Clause #120 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) False % 50.02/50.18 Clause #121 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 50.02/50.18 Clause #126 (by superposition #[121, 84]): ∀ (a a_1 a_2 a_3 : Iota), % 50.02/50.18 Or (Eq True False) % 50.02/50.18 (Or (Eq (convergent_lines (skS.0 0 a) a_1) True) (Eq (convergent_lines (skS.0 2 a a_2 a_3) a_1) True)) % 50.02/50.20 Clause #127 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), % 50.02/50.20 Or (Eq (Not (unorthogonal_lines a a_1)) True) % 50.02/50.20 (Or (Eq (Not (unorthogonal_lines a_2 a)) False) % 50.02/50.20 (Or (Eq (Not (convergent_lines a_2 a_1)) False) (Eq (convergent_lines a a_1) False))) % 50.02/50.20 Clause #128 (by clausification #[127]): ∀ (a a_1 a_2 : Iota), % 50.02/50.20 Or (Eq (Not (unorthogonal_lines a a_1)) False) % 50.02/50.20 (Or (Eq (Not (convergent_lines a a_2)) False) % 50.02/50.20 (Or (Eq (convergent_lines a_1 a_2) False) (Eq (unorthogonal_lines a_1 a_2) False))) % 50.02/50.20 Clause #129 (by clausification #[128]): ∀ (a a_1 a_2 : Iota), % 50.02/50.20 Or (Eq (Not (convergent_lines a a_1)) False) % 50.02/50.20 (Or (Eq (convergent_lines a_2 a_1) False) % 50.02/50.20 (Or (Eq (unorthogonal_lines a_2 a_1) False) (Eq (unorthogonal_lines a a_2) True))) % 50.02/50.20 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 : Iota), % 50.02/50.20 Or (Eq (convergent_lines a a_1) False) % 50.02/50.20 (Or (Eq (unorthogonal_lines a a_1) False) % 50.02/50.20 (Or (Eq (unorthogonal_lines a_2 a) True) (Eq (convergent_lines a_2 a_1) True))) % 50.02/50.20 Clause #132 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Eq (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 50.02/50.20 Clause #133 (by clausification #[126]): ∀ (a a_1 a_2 a_3 : Iota), % 50.02/50.20 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) (Eq (convergent_lines (skS.0 2 a a_2 a_3) a_1) True) % 50.02/50.20 Clause #138 (by superposition #[133, 84]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 50.02/50.20 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) % 50.02/50.20 (Or (Eq True False) (Or (Eq (convergent_lines (skS.0 2 a a_2 a_3) a_4) True) (Eq (convergent_lines a_1 a_4) True))) % 50.02/50.20 Clause #182 (by clausification #[138]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 50.02/50.20 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) % 50.02/50.20 (Or (Eq (convergent_lines (skS.0 2 a a_2 a_3) a_4) True) (Eq (convergent_lines a_1 a_4) True)) % 50.02/50.20 Clause #183 (by superposition #[182, 120]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 50.02/50.20 Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) a_3) True) % 50.02/50.20 (Or (Eq (convergent_lines (skS.0 1 a a_4) a_3) True) (Eq True False)) % 50.02/50.20 Clause #224 (by clausification #[183]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 50.02/50.20 Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (convergent_lines (skS.0 1 a a_4) a_3) True) % 50.02/50.20 Clause #225 (by superposition #[224, 19]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) True) (Eq True False) % 50.02/50.20 Clause #234 (by superposition #[224, 19]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) True) (Eq True False) % 50.02/50.20 Clause #243 (by clausification #[234]): ∀ (a a_1 a_2 a_3 : Iota), Eq (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) True % 50.02/50.20 Clause #249 (by superposition #[243, 130]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 50.02/50.20 Or (Eq True False) % 50.02/50.20 (Or (Eq (unorthogonal_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) False) % 50.02/50.20 (Or (Eq (unorthogonal_lines a_4 (skS.0 2 a a_1 a_2)) True) (Eq (convergent_lines a_4 (skS.0 1 a a_3)) True))) % 50.02/50.20 Clause #252 (by clausification #[225]): ∀ (a a_1 a_2 a_3 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) True % 50.02/50.20 Clause #258 (by superposition #[252, 130]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 50.02/50.20 Or (Eq True False) % 50.02/50.20 (Or (Eq (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) False) % 50.02/50.20 (Or (Eq (unorthogonal_lines a_4 (skS.0 1 a a_1)) True) (Eq (convergent_lines a_4 (skS.0 2 a a_2 a_3)) True))) % 50.02/50.20 Clause #4322 (by clausification #[249]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 50.02/50.20 Or (Eq (unorthogonal_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) False) % 50.02/50.20 (Or (Eq (unorthogonal_lines a_4 (skS.0 2 a a_1 a_2)) True) (Eq (convergent_lines a_4 (skS.0 1 a a_3)) True)) % 50.02/50.20 Clause #4733 (by clausification #[258]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 50.02/50.20 Or (Eq (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) False) % 50.02/50.20 (Or (Eq (unorthogonal_lines a_4 (skS.0 1 a a_1)) True) (Eq (convergent_lines a_4 (skS.0 2 a a_2 a_3)) True)) % 50.02/50.20 Clause #4734 (by superposition #[4733, 132]): ∀ (a a_1 a_2 a_3 : Iota), % 50.02/50.20 Or (Eq (unorthogonal_lines a (skS.0 1 a_1 a_2)) True) % 50.02/50.20 (Or (Eq (convergent_lines a (skS.0 2 a_1 a_2 a_3)) True) (Eq False True)) % 50.02/50.20 Clause #4779 (by clausification #[4734]): ∀ (a a_1 a_2 a_3 : Iota), % 50.10/50.27 Or (Eq (unorthogonal_lines a (skS.0 1 a_1 a_2)) True) (Eq (convergent_lines a (skS.0 2 a_1 a_2 a_3)) True) % 50.10/50.27 Clause #4780 (by superposition #[4779, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (unorthogonal_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq True False) % 50.10/50.27 Clause #4789 (by clausification #[4780]): ∀ (a a_1 a_2 : Iota), Eq (unorthogonal_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 50.10/50.27 Clause #4790 (by superposition #[4789, 4322]): ∀ (a a_1 a_2 a_3 : Iota), % 50.10/50.27 Or (Eq True False) % 50.10/50.27 (Or (Eq (unorthogonal_lines a (skS.0 2 a_1 a_2 a_3)) True) (Eq (convergent_lines a (skS.0 1 a_1 a_2)) True)) % 50.10/50.27 Clause #4803 (by clausification #[4790]): ∀ (a a_1 a_2 a_3 : Iota), % 50.10/50.27 Or (Eq (unorthogonal_lines a (skS.0 2 a_1 a_2 a_3)) True) (Eq (convergent_lines a (skS.0 1 a_1 a_2)) True) % 50.10/50.27 Clause #4804 (by superposition #[4803, 43]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False) % 50.10/50.27 Clause #4827 (by clausification #[4804]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 50.10/50.27 Clause #4828 (by superposition #[4827, 120]): Eq True False % 50.10/50.27 Clause #4884 (by clausification #[4828]): False % 50.10/50.27 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------